pyx/deco.py

   1 #!/usr/bin/env python
   2 # -*- coding: ISO-8859-1 -*-
   3 #
   4 #
   5 # Copyright (C) 2002-2004 Jörg Lehmann <joergl@users.sourceforge.net>
   6 # Copyright (C) 2003-2004 Michael Schindler <m-schindler@users.sourceforge.net>
   7 # Copyright (C) 2002-2004 André Wobst <wobsta@users.sourceforge.net>
   8 #
   9 # This file is part of PyX (http://pyx.sourceforge.net/).
  10 #
  11 # PyX is free software; you can redistribute it and/or modify
  12 # it under the terms of the GNU General Public License as published by
  13 # the Free Software Foundation; either version 2 of the License, or
  14 # (at your option) any later version.
  15 #
  16 # PyX is distributed in the hope that it will be useful,
  17 # but WITHOUT ANY WARRANTY; without even the implied warranty of
  18 # MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
  19 # GNU General Public License for more details.
  20 #
  21 # You should have received a copy of the GNU General Public License
  22 # along with PyX; if not, write to the Free Software
  23 # Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
  24
  25 # TODO:
  26 # - should we improve on the arc length -> arg parametrization routine or
  27 #   should we at least factor it out?
  28
  29 import sys, math
  30 import attr, base, canvas, color, helper, path, style, trafo, unit
  31
  32 #
  33 # Decorated path
  34 #
  35
  36 class decoratedpath(base.PSCmd):
  37     """Decorated path
  38
  39     The main purpose of this class is during the drawing
  40     (stroking/filling) of a path. It collects attributes for the
  41     stroke and/or fill operations.
  42     """
  43
  44     def __init__(self, path, strokepath=None, fillpath=None,
  45                  styles=None, strokestyles=None, fillstyles=None,
  46                  subcanvas=None):
  47
  48         self.path = path
  49
  50         # path to be stroked or filled (or None)
  51         self.strokepath = strokepath
  52         self.fillpath = fillpath
  53
  54         # global style for stroking and filling and subdps
  55         self.styles = helper.ensurelist(styles)
  56
  57         # styles which apply only for stroking and filling
  58         self.strokestyles = helper.ensurelist(strokestyles)
  59         self.fillstyles = helper.ensurelist(fillstyles)
  60
  61         # the canvas can contain additional elements of the path, e.g.,
  62         # arrowheads,
  63         if subcanvas is None:
  64             self.subcanvas = canvas.canvas()
  65         else:
  66             self.subcanvas = subcanvas
  67
  68
  69     def bbox(self):
  70         scbbox = self.subcanvas.bbox()
  71         pbbox = self.path.bbox()
  72         if scbbox is not None:
  73             return scbbox+pbbox
  74         else:
  75             return pbbox
  76
  77     def prolog(self):
  78         result = []
  79         for style in list(self.styles) + list(self.fillstyles) + list(self.strokestyles):
  80             result.extend(style.prolog())
  81         result.extend(self.subcanvas.prolog())
  82         return result
  83
  84     def outputPS(self, file):
  85         # draw (stroke and/or fill) the decoratedpath on the canvas
  86         # while trying to produce an efficient output, e.g., by
  87         # not writing one path two times
  88
  89         # small helper
  90         def _writestyles(styles, file=file):
  91             for style in styles:
  92                 style.outputPS(file)
  93
  94         # apply global styles
  95         if self.styles:
  96             file.write("gsave\n")
  97             _writestyles(self.styles)
  98
  99         if self.fillpath is not None:
 100             file.write("newpath\n")
 101             self.fillpath.outputPS(file)
 102
 103             if self.strokepath==self.fillpath:
 104                 # do efficient stroking + filling
 105                 file.write("gsave\n")
 106
 107                 if self.fillstyles:
 108                     _writestyles(self.fillstyles)
 109
 110                 file.write("fill\n")
 111                 file.write("grestore\n")
 112
 113                 if self.strokestyles:
 114                     file.write("gsave\n")
 115                     _writestyles(self.strokestyles)
 116
 117                 file.write("stroke\n")
 118
 119                 if self.strokestyles:
 120                     file.write("grestore\n")
 121             else:
 122                 # only fill fillpath - for the moment
 123                 if self.fillstyles:
 124                     file.write("gsave\n")
 125                     _writestyles(self.fillstyles)
 126
 127                 file.write("fill\n")
 128
 129                 if self.fillstyles:
 130                     file.write("grestore\n")
 131
 132         if self.strokepath is not None and self.strokepath!=self.fillpath:
 133             # this is the only relevant case still left
 134             # Note that a possible stroking has already been done.
 135
 136             if self.strokestyles:
 137                 file.write("gsave\n")
 138                 _writestyles(self.strokestyles)
 139
 140             file.write("newpath\n")
 141             self.strokepath.outputPS(file)
 142             file.write("stroke\n")
 143
 144             if self.strokestyles:
 145                 file.write("grestore\n")
 146
 147         if self.strokepath is None and self.fillpath is None:
 148             raise RuntimeError("Path neither to be stroked nor filled")
 149
 150         # now, draw additional elements of decoratedpath
 151         self.subcanvas.outputPS(file)
 152
 153         # restore global styles
 154         if self.styles:
 155             file.write("grestore\n")
 156
 157     def outputPDF(self, file):
 158         # draw (stroke and/or fill) the decoratedpath on the canvas
 159
 160         def _writestyles(styles, file=file):
 161             for style in styles:
 162                 style.outputPDF(file)
 163
 164         def _writestrokestyles(strokestyles, file=file):
 165             for style in strokestyles:
 166                 if isinstance(style, color.color):
 167                     style.outputPDF(file, fillattr=0)
 168                 else:
 169                     style.outputPDF(file)
 170
 171         def _writefillstyles(fillstyles, file=file):
 172             for style in fillstyles:
 173                 if isinstance(style, color.color):
 174                     style.outputPDF(file, strokeattr=0)
 175                 else:
 176                     style.outputPDF(file)
 177
 178         # apply global styles
 179         if self.styles:
 180             file.write("q\n") # gsave
 181             _writestyles(self.styles)
 182
 183         if self.fillpath is not None:
 184             self.fillpath.outputPDF(file)
 185
 186             if self.strokepath==self.fillpath:
 187                 # do efficient stroking + filling
 188                 file.write("q\n") # gsave
 189
 190                 if self.fillstyles:
 191                     _writefillstyles(self.fillstyles)
 192                 if self.strokestyles:
 193                     _writestrokestyles(self.strokestyles)
 194
 195                 file.write("B\n") # both stroke and fill
 196                 file.write("Q\n") # grestore
 197             else:
 198                 # only fill fillpath - for the moment
 199                 if self.fillstyles:
 200                     file.write("q\n") # gsave
 201                     _writefillstyles(self.fillstyles)
 202
 203                 file.write("f\n") # fill
 204
 205                 if self.fillstyles:
 206                     file.write("Q\n") # grestore
 207
 208         if self.strokepath is not None and self.strokepath!=self.fillpath:
 209             # this is the only relevant case still left
 210             # Note that a possible stroking has already been done.
 211
 212             if self.strokestyles:
 213                 file.write("q\n") # gsave
 214                 _writestrokestyles(self.strokestyles)
 215
 216             self.strokepath.outputPDF(file)
 217             file.write("S\n") # stroke
 218
 219             if self.strokestyles:
 220                 file.write("Q\n") # grestore
 221
 222         if self.strokepath is None and self.fillpath is None:
 223             raise RuntimeError("Path neither to be stroked nor filled")
 224
 225         # now, draw additional elements of decoratedpath
 226         self.subcanvas.outputPDF(file)
 227
 228         # restore global styles
 229         if self.styles:
 230             file.write("Q\n") # grestore
 231
 232 #
 233 # Path decorators
 234 #
 235
 236 class deco:
 237
 238     """decorators
 239
 240     In contrast to path styles, path decorators depend on the concrete
 241     path to which they are applied. In particular, they don't make
 242     sense without any path and can thus not be used in canvas.set!
 243
 244     """
 245
 246     def decorate(self, dp):
 247         """apply a style to a given decoratedpath object dp
 248
 249         decorate accepts a decoratedpath object dp, applies PathStyle
 250         by modifying dp in place and returning the new dp.
 251         """
 252
 253         pass
 254
 255 #
 256 # stroked and filled: basic decos which stroked and fill,
 257 # respectively the path
 258 #
 259
 260 class _stroked(deco, attr.exclusiveattr):
 261
 262     """stroked is a decorator, which draws the outline of the path"""
 263
 264     def __init__(self, styles=[]):
 265         attr.exclusiveattr.__init__(self, _stroked)
 266         self.styles = attr.mergeattrs(styles)
 267         attr.checkattrs(self.styles, [style.strokestyle])
 268
 269     def __call__(self, styles=[]):
 270         # XXX or should we also merge self.styles
 271         return _stroked(styles)
 272
 273     def decorate(self, dp):
 274         dp.strokepath = dp.path
 275         dp.strokestyles = self.styles
 276         return dp
 277
 278 stroked = _stroked()
 279 stroked.clear = attr.clearclass(_stroked)
 280
 281
 282 class _filled(deco, attr.exclusiveattr):
 283
 284     """filled is a decorator, which fills the interior of the path"""
 285
 286     def __init__(self, styles=[]):
 287         attr.exclusiveattr.__init__(self, _filled)
 288         self.styles = attr.mergeattrs(styles)
 289         attr.checkattrs(self.styles, [style.fillstyle])
 290
 291     def __call__(self, styles=[]):
 292         # XXX or should we also merge self.styles
 293         return _filled(styles)
 294
 295     def decorate(self, dp):
 296         dp.fillpath = dp.path
 297         dp.fillstyles = self.styles
 298         return dp
 299
 300 filled = _filled()
 301 filled.clear = attr.clearclass(_filled)
 302
 303 #
 304 # Arrows
 305 #
 306
 307 # two helper functions which construct the arrowhead and return its size, respectively
 308
 309 def _arrowheadtemplatelength(anormpath, size):
 310     "calculate length of arrowhead template (in parametrisation of anormpath)"
 311     # get tip (tx, ty)
 312     tx, ty = anormpath.begin()
 313
 314     # obtain arrow template by using path up to first intersection
 315     # with circle around tip (as suggested by Michael Schindler)
 316     ipar = anormpath.intersect(path.circle(tx, ty, size))
 317     if ipar[0]:
 318         alen = ipar[0][0]
 319     else:
 320         # if this doesn't work, use first order conversion from pts to
 321         # the bezier curve's parametrization
 322         tvec = anormpath.tangent(0)
 323         tlen = tvec.arclen_pt()
 324         try:
 325             alen = unit.topt(size)/tlen
 326         except ArithmeticError:
 327             # take maximum, we can get
 328             alen = anormpath.range()
 329         if alen > anormpath.range(): alen = anormpath.range()
 330
 331     return alen
 332
 333
 334 def _arrowhead(anormpath, size, angle, constriction):
 335
 336     """helper routine, which returns an arrowhead for a normpath
 337
 338     returns arrowhead at begin of anormpath with size,
 339     opening angle and relative constriction
 340     """
 341
 342     alen = _arrowheadtemplatelength(anormpath, size)
 343     tx, ty = anormpath.begin()
 344
 345     # now we construct the template for our arrow but cutting
 346     # the path a the corresponding length
 347     arrowtemplate = anormpath.split([alen])[0]
 348
 349     # from this template, we construct the two outer curves
 350     # of the arrow
 351     arrowl = arrowtemplate.transformed(trafo.rotate(-angle/2.0, tx, ty))
 352     arrowr = arrowtemplate.transformed(trafo.rotate( angle/2.0, tx, ty))
 353
 354     # now come the joining backward parts
 355     if constriction:
 356         # arrow with constriction
 357
 358         # constriction point (cx, cy) lies on path
 359         cx, cy = anormpath.at(constriction*alen)
 360
 361         arrowcr= path.line(*(arrowr.end()+(cx,cy)))
 362
 363         arrow = arrowl.reversed() << arrowr << arrowcr
 364         arrow.append(path.closepath())
 365     else:
 366         # arrow without constriction
 367         arrow = arrowl.reversed() << arrowr
 368         arrow.append(path.closepath())
 369
 370     return arrow
 371
 372
 373 _base = 6 * unit.v_pt
 374
 375 class arrow(deco, attr.attr):
 376
 377     """arrow is a decorator which adds an arrow to either side of the path"""
 378
 379     def __init__(self, attrs=[], position=0, size=_base, angle=45, constriction=0.8):
 380         self.attrs = attr.mergeattrs([style.linestyle.solid, filled] + attrs)
 381         attr.checkattrs(self.attrs, [deco, style.fillstyle, style.strokestyle])
 382         self.position = position
 383         self.size = unit.length(size, default_type="v")
 384         self.angle = angle
 385         self.constriction = constriction
 386
 387     def __call__(self, attrs=None, position=None, size=None, angle=None, constriction=None):
 388         if attrs is None:
 389             attrs = self.attrs
 390         if position is None:
 391             position = self.position
 392         if size is None:
 393             size = self.size
 394         if angle is None:
 395             angle = self.angle
 396         if constriction is None:
 397             constriction = self.constriction
 398         return arrow(attrs=attrs, position=position, size=size, angle=angle, constriction=constriction)
 399
 400     def decorate(self, dp):
 401         # XXX raise exception error, when strokepath is not defined
 402
 403         # convert to normpath if necessary
 404         if isinstance(dp.strokepath, path.normpath):
 405             anormpath = dp.strokepath
 406         else:
 407             anormpath = path.normpath(dp.path)
 408         if self.position:
 409             anormpath = anormpath.reversed()
 410
 411         # add arrowhead to decoratedpath
 412         dp.subcanvas.draw(_arrowhead(anormpath, self.size, self.angle, self.constriction),
 413                           self.attrs)
 414
 415         # calculate new strokepath
 416         alen = _arrowheadtemplatelength(anormpath, self.size)
 417         if self.constriction:
 418             ilen = alen*self.constriction
 419         else:
 420             ilen = alen
 421
 422         # correct somewhat for rotation of arrow segments
 423         ilen = ilen*math.cos(math.pi*self.angle/360.0)
 424
 425         # this is the rest of the path, we have to draw
 426         anormpath = anormpath.split([ilen])[1]
 427
 428         # go back to original orientation, if necessary
 429         if self.position:
 430             anormpath.reverse()
 431
 432         # set the new (shortened) strokepath
 433         dp.strokepath = anormpath
 434
 435         return dp
 436
 437 arrow.clear = attr.clearclass(arrow)
 438
 439 # arrows at begin of path
 440 barrow = arrow(position=0)
 441 barrow.SMALL = barrow(size=_base/math.sqrt(64))
 442 barrow.SMALl = barrow(size=_base/math.sqrt(32))
 443 barrow.SMAll = barrow(size=_base/math.sqrt(16))
 444 barrow.SMall = barrow(size=_base/math.sqrt(8))
 445 barrow.Small = barrow(size=_base/math.sqrt(4))
 446 barrow.small = barrow(size=_base/math.sqrt(2))
 447 barrow.normal = barrow(size=_base)
 448 barrow.large = barrow(size=_base*math.sqrt(2))
 449 barrow.Large = barrow(size=_base*math.sqrt(4))
 450 barrow.LArge = barrow(size=_base*math.sqrt(8))
 451 barrow.LARge = barrow(size=_base*math.sqrt(16))
 452 barrow.LARGe = barrow(size=_base*math.sqrt(32))
 453 barrow.LARGE = barrow(size=_base*math.sqrt(64))
 454
 455 # arrows at end of path
 456 earrow = arrow(position=1)
 457 earrow.SMALL = earrow(size=_base/math.sqrt(64))
 458 earrow.SMALl = earrow(size=_base/math.sqrt(32))
 459 earrow.SMAll = earrow(size=_base/math.sqrt(16))
 460 earrow.SMall = earrow(size=_base/math.sqrt(8))
 461 earrow.Small = earrow(size=_base/math.sqrt(4))
 462 earrow.small = earrow(size=_base/math.sqrt(2))
 463 earrow.normal = earrow(size=_base)
 464 earrow.large = earrow(size=_base*math.sqrt(2))
 465 earrow.Large = earrow(size=_base*math.sqrt(4))
 466 earrow.LArge = earrow(size=_base*math.sqrt(8))
 467 earrow.LARge = earrow(size=_base*math.sqrt(16))
 468 earrow.LARGe = earrow(size=_base*math.sqrt(32))
 469 earrow.LARGE = earrow(size=_base*math.sqrt(64))
 470
 471
 472 class cycloid(deco, attr.attr):
 473     """Wraps a cycloid around a path.
 474
 475     The outcome looks like a metal spring with the originalpath as the axis.
 476     """
 477
 478     def __init__(self, radius=0.5, loops=10, skipfirst=1, skiplast=1, curvesperloop=2, left=1):
 479         self.skipfirst = unit.length(skipfirst, default_type="v")
 480         self.skiplast = unit.length(skiplast, default_type="v")
 481         self.radius = unit.length(radius, default_type="v")
 482         self.halfloops = 2 * int(loops) + 1
 483         self.curvesperhloop = int(0.5 * curvesperloop)
 484         self.sign = left and 1 or -1
 485
 486     def __call__(self, radius=None, loops=None, skipfirst=None, skiplast=None, curvesperloop=None, left=None):
 487         if radius is None:
 488             radius = self.radius
 489         if loops is None:
 490             loops = int(0.5 * self.halfloops)
 491         if skipfirst is None:
 492             skipfirst = self.skipfirst
 493         if skiplast is None:
 494             skiplast = self.skiplast
 495         if curvesperloop is None:
 496             curvesperloop = self.curvesperloop
 497         if left is None:
 498             left = self.left
 499         return cycloid(radius=radius, loops=loop, skipfirst=skipfirst, skiplast=skiplast,
 500                        curvesperloop=curvesperloop, left=left)
 501
 502     def decorate(self, dp):
 503         # XXX: is this the correct way to select the basepath???!!!
 504         if isinstance(dp.strokepath, path.normpath):
 505             basepath = dp.strokepath
 506         elif dp.strokepath is not None:
 507             basepath = path.normpath(dp.strokepath)
 508         elif isinstance(dp.path, path.normpath):
 509             basepath = dp.path
 510         else:
 511             basepath = path.normpath(dp.path)
 512
 513         skipfirst = abs(unit.topt(self.skipfirst))
 514         skiplast = abs(unit.topt(self.skiplast))
 515         radius = abs(unit.topt(self.radius))
 516
 517         # make list of the lengths and parameters at points on basepath where we will add cycloid-points
 518         totlength = basepath.arclen_pt()
 519         if totlength < skipfirst + skiplast + radius:
 520             raise RuntimeError("Path is too short for decoration with cycloid")
 521
 522         # differences in length, angle ... between two basepoints
 523         # and between basepoints and controlpoints
 524         Dphi = math.pi / self.curvesperhloop
 525         Dlength = (totlength - skipfirst - skiplast - 2*radius) * 1.0 / (self.halfloops * self.curvesperhloop)
 526         # from path._arctobcurve:
 527         # optimal relative distance along tangent for second and third control point
 528         l = 4 * (1 - math.cos(Dphi/2)) / (3 * math.sin(Dphi/2))
 529         controlDphi = math.atan2(l, 1.0)
 530         controlDlength = Dlength * controlDphi / Dphi
 531
 532         # for every point on the cycloid we need the basepoint and two controlpoints
 533         lengths = [skipfirst + radius + i * Dlength for i in range(self.halfloops * self.curvesperhloop + 1)]
 534         lengths[0] = skipfirst
 535         lengths[-1] = totlength - skiplast
 536         phis = [i * Dphi for i in range(self.halfloops * self.curvesperhloop + 1)]
 537         params = basepath.arclentoparam_pt(lengths)
 538
 539         #for param in params:
 540         #    dp.subcanvas.fill(path.circle_pt(*(basepath.at_pt(param) + (0.3,))), [color.rgb.blue])
 541         #    dp.subcanvas.fill(path.circle_pt(*(basepath.at_pt(param) + (0.3,))), [color.rgb.blue])
 542         #    dp.subcanvas.fill(path.circle_pt(*(basepath.at_pt(param) + (0.3,))), [color.rgb.red])
 543
 544         # get the positions of the splitpoints in the cycloid
 545         points = []
 546         for phi, param, length in zip(phis, params, lengths):
 547             # the cycloid is a circle that is stretched along the basepath
 548             # here are the points of that circle
 549             basetrafo = basepath.trafo(param)
 550             basex, basey = -radius * math.cos(phi), radius * math.sin(phi)
 551             preex, preey = basex - l * basey, basey + l * basex
 552             postx, posty = basex + l * basey, basey - l * basex
 553             # and put everything at the proper place
 554             preex = preex - controlDlength
 555             postx = postx + controlDlength
 556             if length is lengths[0]:
 557                 postx += radius
 558             if length is lengths[-1]:
 559                 basex, preex = basex - radius, preex - radius
 560             points.append(basetrafo._apply(preex, self.sign * preey) +
 561                           basetrafo._apply(basex, self.sign * basey) +
 562                           basetrafo._apply(postx, self.sign * posty))
 563
 564         cycloidpath = basepath.split([params[0]])[0]
 565         if len(points) > 1:
 566             cycloidpath.append(path.multicurveto_pt(
 567                 [(points[i][4:6] + points[i+1][0:4]) for i in range(len(points)-1)]))
 568         else:
 569             raise RuntimeError("Not enough points while decorating with cycloid")
 570         cycloidpath.joined(basepath.split([params[-1]])[-1])
 571
 572         # store cycloid path
 573         # XXX bbox of dp.path is wrong
 574         dp.strokepath = cycloidpath
 575         return dp
 576
 577
 578 class smoothed(deco, attr.attr):
 579
 580     """Bends corners in a path.
 581
 582     This decorator replaces corners in a path with bezier curves. There are two cases:
 583     - If the corner lies between two lines, _two_ bezier curves will be used
 584       that are highly optimized to look good (their curvature is to be zero at the ends
 585       and has to have zero derivative in the middle).
 586       Additionally, it can controlled by the softness-parameter.
 587     - If the corner lies between curves then _one_ bezier is used that is (except in some
 588       special cases) uniquely determined by the tangents and curvatures at its end-points.
 589       In some cases it is necessary to use only the absolute value of the curvature to avoid a
 590       cusp-shaped connection of the new bezier to the old path. In this case the use of
 591       "strict=0" allows the sign of the curvature to switch.
 592     - The radius argument gives the arclength-distance of the corner to the points where the
 593       old path is cut and the beziers are inserted.
 594     - Path elements that are too short (shorter than the radius) are skipped
 595     """
 596
 597     def __init__(self, radius, softness=1, strict=0):
 598         self.radius = unit.length(radius, default_type="v")
 599         self.softness = softness
 600         self.strict = strict
 601
 602     def __call__(self, radius=None, softness=None, strict=None):
 603         if radius is None:
 604             radius = self.radius
 605         if softness is None:
 606             softness = self.softness
 607         if strict is None:
 608             strict = self.strict
 609         return smoothed(radius=radius, softness=softness, strict=strict)
 610
 611     def _twobeziersbetweentolines(self, B, tangent1, tangent2, r1, r2, softness=1):
 612         # Takes the corner B
 613         # and two tangent vectors heading to and from B
 614         # and two radii r1 and r2:
 615         # All arguments must be in Points
 616         # Returns the seven control points of the two bezier curves:
 617         #  - start d1
 618         #  - control points g1 and f1
 619         #  - midpoint e
 620         #  - control points f2 and g2
 621         #  - endpoint d2
 622
 623         # make direction vectors d1: from B to A
 624         #                        d2: from B to C
 625         d1 = -tangent1[0] / math.hypot(*tangent1), -tangent1[1] / math.hypot(*tangent1)
 626         d2 =  tangent2[0] / math.hypot(*tangent2),  tangent2[1] / math.hypot(*tangent2)
 627
 628         # 0.3192 has turned out to be the maximum softness available
 629         # for straight lines ;-)
 630         f = 0.3192 * softness
 631         g = (15.0 * f + math.sqrt(-15.0*f*f + 24.0*f))/12.0
 632
 633         # make the control points
 634         f1 = B[0] + f * r1 * d1[0], B[1] + f * r1 * d1[1]
 635         f2 = B[0] + f * r2 * d2[0], B[1] + f * r2 * d2[1]
 636         g1 = B[0] + g * r1 * d1[0], B[1] + g * r1 * d1[1]
 637         g2 = B[0] + g * r2 * d2[0], B[1] + g * r2 * d2[1]
 638         d1 = B[0] +     r1 * d1[0], B[1] +     r1 * d1[1]
 639         d2 = B[0] +     r2 * d2[0], B[1] +     r2 * d2[1]
 640         e  = 0.5 * (f1[0] + f2[0]), 0.5 * (f1[1] + f2[1])
 641
 642         return [d1, g1, f1, e, f2, g2, d2]
 643
 644     def _onebezierbetweentwopathels(self, A, B, tangentA, tangentB, curvA, curvB, strict=0):
 645         # connects points A and B with a bezier curve that has
 646         # prescribed tangents dirA, dirB and curvatures curA, curB.
 647         # If strict, the sign of the curvature will be forced which may invert
 648         # the sign of the tangents. If not strict, the sign of the curvature may
 649         # be switched but the tangent may not.
 650
 651         def sign(x):
 652             try: return abs(x) / x
 653             except ZeroDivisionError: return 0
 654
 655         # normalise the tangent vectors
 656         dirA = (tangentA[0] / math.hypot(*tangentA), tangentA[1] / math.hypot(*tangentA))
 657         dirB = (tangentB[0] / math.hypot(*tangentB), tangentB[1] / math.hypot(*tangentB))
 658         # some shortcuts
 659         T = dirA[0] * dirB[1] - dirA[1] * dirB[0]
 660         D = 3 * (dirA[0] * (B[1]-A[1]) - dirA[1] * (B[0]-A[0]))
 661         E = 3 * (dirB[0] * (B[1]-A[1]) - dirB[1] * (B[0]-A[0]))
 662         # the variables: \dot X(0) = a * dirA
 663         #                \dot X(1) = b * dirB
 664         a, b = None, None
 665
 666         # ask for some special cases:
 667         # Newton iteration is likely to fail if T==0 or curvA,curvB==0
 668         if abs(T) < 1e-10:
 669             try:
 670                 a = 2.0 * D / curvA
 671                 a = math.sqrt(abs(a)) * sign(a)
 672                 b = -2.0 * E / curvB
 673                 b = math.sqrt(abs(b)) * sign(b)
 674             except ZeroDivisionError:
 675                 sys.stderr.write("*** PyX Warning: The connecting bezier is not uniquely determined. "
 676                     "The simple heuristic solution may not be optimal.\n")
 677                 a = b = 1.5 * math.hypot(A[0] - B[0], A[1] - B[1])
 678         else:
 679             if abs(curvA) < 1.0e-4:
 680                 b = D / T
 681                 a = - (E + b*abs(b)*curvB*0.5) / T
 682             elif abs(curvB) < 1.0e-4:
 683                 a = -E / T
 684                 b = (D - a*abs(a)*curvA*0.5) / T
 685             else:
 686                 a, b = None, None
 687
 688         # do the general case: Newton iteration
 689         if a is None:
 690             # solve the coupled system
 691             #     0 = Ga(a,b) = 0.5 a |a| curvA + b * T - D
 692             #     0 = Gb(a,b) = 0.5 b |b| curvB + a * T + E
 693             # this system is equivalent to the geometric contraints:
 694             #     the curvature and the normal tangent vectors
 695             #     at parameters 0 and 1 are to be continuous
 696             # the system is solved by 2-dim Newton-Iteration
 697             # (a,b)^{i+1} = (a,b)^i - (DG)^{-1} (Ga(a^i,b^i), Gb(a^i,b^i))
 698             a = b = 0
 699             Ga = Gb = 1
 700             while max(abs(Ga),abs(Gb)) > 1.0e-5:
 701                 detDG = abs(a*b) * curvA*curvB - T*T
 702                 invDG = [[curvB*abs(b)/detDG, -T/detDG], [-T/detDG, curvA*abs(a)/detDG]]
 703
 704                 Ga = a*abs(a)*curvA*0.5 + b*T - D
 705                 Gb = b*abs(b)*curvB*0.5 + a*T + E
 706
 707                 a, b = a - 0.5*invDG[0][0]*Ga - 0.5*invDG[0][1]*Gb, b - 0.5*invDG[1][0]*Ga - 0.5*invDG[1][1]*Gb
 708
 709         # the curvature may change its sign if we would get a cusp
 710         # in the optimal case we have a>0 and b>0
 711         if not strict:
 712             a, b = abs(a), abs(b)
 713
 714         return [A, (A[0] + a * dirA[0] / 3.0, A[1] + a * dirA[1] / 3.0),
 715                    (B[0] - b * dirB[0] / 3.0, B[1] - b * dirB[1] / 3.0), B]
 716
 717
 718     def decorate(self, dp):
 719         radius = unit.topt(self.radius)
 720         # XXX: is this the correct way to select the basepath???!!!
 721         # compare to wriggle()
 722         if isinstance(dp.strokepath, path.normpath):
 723             basepath = dp.strokepath
 724         elif dp.strokepath is not None:
 725             basepath = path.normpath(dp.strokepath)
 726         elif isinstance(dp.path, path.normpath):
 727             basepath = dp.path
 728         else:
 729             basepath = path.normpath(dp.path)
 730
 731         newpath = path.path()
 732         for normsubpath in basepath.subpaths:
 733             npels = normsubpath.normpathels
 734             arclens = [npel.arclen_pt() for npel in npels]
 735
 736             # 1. Build up a list of all relevant normpathels
 737             #    and the lengths where they will be cut (length with respect to the normsubpath)
 738             npelnumbers = []
 739             cumalen = 0
 740             for no in range(len(arclens)):
 741                 alen = arclens[no]
 742                 # a first selection criterion for skipping too short normpathels
 743                 # the rest will queeze the radius
 744                 if alen > radius:
 745                     npelnumbers.append(no)
 746                 else:
 747                     sys.stderr.write("*** PyX Warning: smoothed is skipping a normpathel that is too short\n")
 748                 cumalen += alen
 749             # XXX: what happens, if 0 or -1 is skipped and path not closed?
 750
 751             # 2. Find the parameters, points,
 752             #    and calculate tangents and curvatures
 753             params, tangents, curvatures, points = [], [], [], []
 754             for no in npelnumbers:
 755                 npel = npels[no]
 756                 alen = arclens[no]
 757
 758                 # find the parameter(s): either one or two
 759                 if no is npelnumbers[0] and not normsubpath.closed:
 760                     pars = npel._arclentoparam_pt([max(0, alen - radius)])[0]
 761                 elif alen > 2 * radius:
 762                     pars = npel._arclentoparam_pt([radius, alen - radius])[0]
 763                 else:
 764                     pars = npel._arclentoparam_pt([0.5 * alen])[0]
 765
 766                 # find points, tangents and curvatures
 767                 ts,cs,ps = [],[],[]
 768                 for par in pars:
 769                     # XXX: there is no trafo method for normpathels?
 770                     thetrafo = normsubpath.trafo(par + no)
 771                     p = thetrafo._apply(0,0)
 772                     t = thetrafo._apply(1,0)
 773                     ps.append(p)
 774                     ts.append((t[0]-p[0], t[1]-p[1]))
 775                     c = npel.curvradius_pt(par)
 776                     if c is None: cs.append(0)
 777                     else: cs.append(1.0/c)
 778
 779                 params.append(pars)
 780                 points.append(ps)
 781                 tangents.append(ts)
 782                 curvatures.append(cs)
 783
 784             do_moveto = 1 # we do not know yet where to moveto
 785             # 3. First part of extra handling of closed paths
 786             if not normsubpath.closed:
 787                 bpart = npels[npelnumbers[0]].split(params[0])[0]
 788                 if do_moveto:
 789                     newpath.append(path.moveto_pt(*bpart.begin_pt()))
 790                     do_moveto = 0
 791                 if isinstance(bpart, path.normline):
 792                     newpath.append(path.lineto_pt(*bpart.end_pt()))
 793                 elif isinstance(bpart, path.normcurve):
 794                     newpath.append(path.curveto_pt(bpart.x1_pt, bpart.y1_pt, bpart.x2_pt, bpart.y2_pt, bpart.x3_pt, bpart.y3_pt))
 795                 do_moveto = 0
 796
 797             # 4. Do the splitting for the first to the last element,
 798             #    a closed path must be closed later
 799             for i in range(len(npelnumbers)-1+(normsubpath.closed==1)):
 800                 this = npelnumbers[i]
 801                 next = npelnumbers[(i+1) % len(npelnumbers)]
 802                 thisnpel, nextnpel = npels[this], npels[next]
 803
 804                 # split thisnpel apart and take the middle peace
 805                 if len(points[this]) == 2:
 806                     mpart = thisnpel.split(params[this])[1]
 807                     if do_moveto:
 808                         newpath.append(path.moveto_pt(*mpart.begin_pt()))
 809                         do_moveto = 0
 810                     if isinstance(mpart, path.normline):
 811                         newpath.append(path.lineto_pt(*mpart.end_pt()))
 812                     elif isinstance(mpart, path.normcurve):
 813                         newpath.append(path.curveto_pt(mpart.x1_pt, mpart.y1_pt, mpart.x2_pt, mpart.y2_pt, mpart.x3_pt, mpart.y3_pt))
 814
 815                 # add the curve(s) replacing the corner
 816                 if isinstance(thisnpel, path.normline) and isinstance(nextnpel, path.normline) \
 817                    and (next-this == 1 or (this==0 and next==len(npels)-1)):
 818                     d1,g1,f1,e,f2,g2,d2 = self._twobeziersbetweentolines(
 819                         thisnpel.end_pt(), tangents[this][-1], tangents[next][0],
 820                         math.hypot(points[this][-1][0] - thisnpel.end_pt()[0], points[this][-1][1] - thisnpel.end_pt()[1]),
 821                         math.hypot(points[next][0][0] - nextnpel.begin_pt()[0], points[next][0][1] - nextnpel.begin_pt()[1]),
 822                         softness=self.softness)
 823                     if do_moveto:
 824                         newpath.append(path.moveto_pt(*d1))
 825                         do_moveto = 0
 826                     newpath.append(path.curveto_pt(*(g1 + f1 + e)))
 827                     newpath.append(path.curveto_pt(*(f2 + g2 + d2)))
 828                     #for X in [d1,g1,f1,e,f2,g2,d2]:
 829                     #    dp.subcanvas.fill(path.circle_pt(X[0], X[1], 1.0))
 830                 else:
 831                     if not self.strict:
 832                         # the curvature may have the wrong sign -- produce a heuristic for the sign:
 833                         vx, vy = thisnpel.end_pt()[0] - points[this][-1][0], thisnpel.end_pt()[1] - points[this][-1][1]
 834                         wx, wy = points[next][0][0] - thisnpel.end_pt()[0], points[next][0][1] - thisnpel.end_pt()[1]
 835                         sign = vx * wy - vy * wx
 836                         sign = sign / abs(sign)
 837                         curvatures[this][-1] = sign * abs(curvatures[this][-1])
 838                         curvatures[next][0] = sign * abs(curvatures[next][0])
 839                     A,B,C,D = self._onebezierbetweentwopathels(
 840                         points[this][-1], points[next][0], tangents[this][-1], tangents[next][0],
 841                         curvatures[this][-1], curvatures[next][0], strict=self.strict)
 842                     if do_moveto:
 843                         newpath.append(path.moveto_pt(*A))
 844                         do_moveto = 0
 845                     newpath.append(path.curveto_pt(*(B + C + D)))
 846                     #for X in [A,B,C,D]:
 847                     #    dp.subcanvas.fill(path.circle_pt(X[0], X[1], 1.0))
 848
 849             # 5. Second part of extra handling of closed paths
 850             if normsubpath.closed:
 851                 if do_moveto:
 852                     newpath.append(path.moveto_pt(*dp.strokepath.begin()))
 853                     sys.stderr.write("*** PyXWarning: The whole path has been smoothed away -- sorry\n")
 854                 newpath.append(path.closepath())
 855             else:
 856                 epart = npels[npelnumbers[-1]].split([params[-1][0]])[-1]
 857                 if do_moveto:
 858                     newpath.append(path.moveto_pt(*epart.begin_pt()))
 859                     do_moveto = 0
 860                 if isinstance(epart, path.normline):
 861                     newpath.append(path.lineto_pt(*epart.end_pt()))
 862                 elif isinstance(epart, path.normcurve):
 863                     newpath.append(path.curveto_pt(epart.x1_pt, epart.y1_pt, epart.x2_pt, epart.y2_pt, epart.x3_pt, epart.y3_pt))
 864
 865         dp.strokepath = newpath
 866         return dp
 867
 868 smoothed.clear = attr.clearclass(smoothed)
 869
 870 _base = 1
 871 smoothed.SHARP = smoothed(radius="%f cm" % (_base/math.sqrt(64)))
 872 smoothed.SHARp = smoothed(radius="%f cm" % (_base/math.sqrt(32)))
 873 smoothed.SHArp = smoothed(radius="%f cm" % (_base/math.sqrt(16)))
 874 smoothed.SHarp = smoothed(radius="%f cm" % (_base/math.sqrt(8)))
 875 smoothed.Sharp = smoothed(radius="%f cm" % (_base/math.sqrt(4)))
 876 smoothed.sharp = smoothed(radius="%f cm" % (_base/math.sqrt(2)))
 877 smoothed.normal = smoothed(radius="%f cm" % (_base))
 878 smoothed.round = smoothed(radius="%f cm" % (_base*math.sqrt(2)))
 879 smoothed.Round = smoothed(radius="%f cm" % (_base*math.sqrt(4)))
 880 smoothed.ROund = smoothed(radius="%f cm" % (_base*math.sqrt(8)))
 881 smoothed.ROUnd = smoothed(radius="%f cm" % (_base*math.sqrt(16)))
 882 smoothed.ROUNd = smoothed(radius="%f cm" % (_base*math.sqrt(32)))
 883 smoothed.ROUND = smoothed(radius="%f cm" % (_base*math.sqrt(64)))
 884